CN201851630U - Asymmetric long-tooth profile evolvent planetary gear box - Google Patents

Asymmetric long-tooth profile evolvent planetary gear box Download PDF

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CN201851630U
CN201851630U CN2010205998276U CN201020599827U CN201851630U CN 201851630 U CN201851630 U CN 201851630U CN 2010205998276 U CN2010205998276 U CN 2010205998276U CN 201020599827 U CN201020599827 U CN 201020599827U CN 201851630 U CN201851630 U CN 201851630U
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gear
flank profil
diameter
pressure angle
tooth
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李钊刚
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Abstract

The utility model relates to an improvement of an asymmetric long-tooth profile evolvent planetary gear box, belonging to the technical field of mechanical drive. The asymmetric long-tooth profile evolvent planetary gear box comprises an input shaft and an output shaft which are in transmission connection with each other by mutually-mashed planetary gear systems; a gear of the gear box is provided with gear teeth which are evenly distributed along the periphery; and evolvent tooth profiles are formed at the two sides of the gear teeth and are formed by basic circles with different diameters; and the difference between the work pressure angles at the pitch circles of the work sides and the non-work sides of the gear teeth ranges from 6 degrees to 15 degrees. The limitation of the traditionally-designed standardized basic rack parameter is broken through by the asymmetric long tooth profile evolvent planetary gear box, the double action for reinforcing the tooth profile at a main loaded side and enhancing tooth addendum is realized by weakening the tooth profile at an unloaded side or an under-loaded side, and the technical effects of improving the bearing capability of the gear, lightening the weight of the gear, enlarging the overlap ratio, improving the drive performance, and reducing the running noise and the vibration can be realzed.

Description

Asymmetric long flank profil involute planet gear case
Technical field
The utility model relates to a kind of gear-box, and especially a kind of improvement of involute planet gear case belongs to the mechanical transmissioning technology field.
Background technique
The involute planet gear case is widely used a kind of gearing in the mechanical transmissioning technology field.Owing to adopt a plurality of planetary pinions transmitted loads simultaneously, make power dividing, and reasonably used interior engagement, therefore have many advantages such as compact structure, volume are little, in light weight, transmission efficiency height.
The simplest, also be that the most basic Gear Planet Transmission form is a NGW type single-stage driving, shown in the sketch of Fig. 1.Its basic building block is made up of sun gear, planet wheel, ring gear and planet carrier.The multistage transmission of NGW type gear-box can be 2 grades of planets, 3 grades of planets, 1 grade of planet and adds 1 grade of cylindrical gears, 1 grade of planet and add 2 grades of cylindrical gearss, 2 grades of planets and add 1 grade of cylindrical gears, 3 grades of planets and add 1 grade of cylindrical gears, reach at a high speed that level is the multiple structural types such as multistage planet of cone gear.
In the involute planet gear transmission of above form, no matter be the Involute Gear Pair of outer gearing, still the Involute Gear Pair of interior engagement all has the deficiency of following two aspects.
First, because modern age, the design of involute gear was based upon on the standardized basis of cutter, flank profil is to determine by the standardized Basic rack parameter (modulus, pressure angle, addendum coefficient, tip clearance coefficient, Fillet radius) of one group of preliminary election and the shift in position (modification coefficient) of relative standard's pitch circle.The restriction that adjusted by cutter normalizing parameter and lathe, gear must guarantee that certain contact ratio, tooth top do not come to a point, process not undercut, engagement and do not interfere, available gear parameter just is limited in the less zone (general available Closed Graph is represented), is difficult to make gear to reach optimum performance.In fact, in larger scope gear may not be used outside this zone, and often the parameter of some performance the bests just is present in beyond this zone in larger scope.
Obviously,, the constraint that might break away from traditional design theory and method fully should be arranged also, design nonstandard gear to pursue more performance for producing enough large batch of gear.
The second, the flank profil of the gear teeth both sides of used gear is symmetrical fully.For most gears, the load during clockwise and anticlockwise is different, the just single direction running that has, though what have is bidirectional movement, the time of antiport and load are all much lower than forward.Complete symmetrical tooth Profile Design causes main supporting surface because parameter limit makes performance be restricted, and reverse side does not then cause waste because not using, lack use or underloading use.
The model utility content
The technical problems to be solved in the utility model is: at the shortcoming that above prior art exists, proposes a kind ofly can to improve gear capacity or weight reduction, increasing contact ratio, improve transmission performance, the asymmetric long flank profil involute planet gear case of reduction running noise and vibration.
Technical solution of the present utility model is: a kind of asymmetric long flank profil involute planet gear case, have the input shaft and the output shaft that are in transmission connection by the epicyclic train that is meshing with each other, the gear of described gear-box has the gear teeth that are uniformly distributed along the circumference, described gear teeth both sides are involute profile, wherein: the involute profile of described gear teeth both sides is generated by the different basic circle of diameter, and the difference of the Operating pressure angle at described gear teeth active side and non-working side pitch circle place is 6 °～15 °.
This asymmetric long flank profil gear has been broken through the restriction of the standardization Basic rack parameter of traditional design, by weakening non-stand under load or being subjected to the flank profil of underloading side, have to strengthen main stand under load side flank profil and to increase the double action of addendum, therefore can realize improving gear capacity or weight reduction, increasing contact ratio, improve transmission performance, reduce the technique effect of running noise and vibration.
The utility model further improves: the addendum coefficient of the described gear teeth is greater than 1.0, smaller or equal to 1.45.
The utility model further improves: during the Operating pressure angle of described gear teeth active side 〉=30 °, the transverse contact ratio of active side is 1.2～1.5.And when Operating pressure angle＜18 of described gear teeth active side °, the transverse contact ratio of active side is 1.8～2.5.
The utility model further improves again: the mutual outer gearing of described gear, the root diameter d of its gear teeth F1,2Pressing following formula determines:
d f1、2＝2×(a’-d a2、1/2-C n)
In the formula
d F1,2---the root diameter of small gear, gearwheel
A '---centre distance
d A2,1---the tip diameter of gearwheel, small gear
C n---bottom clearance, by 0.25 modulus (m n) determine.
If the interior mutually engagement of described gear, the root diameter d of its gear teeth F1,2Pressing following formula determines:
d f1＝2×(d a2/2-a’-C n)
d f2＝2×(d a1/2+a’+C n)
In the formula
d F1, d F2---the root diameter of external gear, internal gear
A '---centre distance
d A1, d A2---the tip diameter of external gear, internal gear
C n---bottom clearance, by 0.25 modulus (m n) determine.
Conclude theoretically, the utlity model has following structural feature:
The basic rack tooth profile of 1. described gear both sides is asymmetric flank profil, the involute that the both sides flank profil adopts the different basic circle of diameter to generate, the engagement of main active side flank profil is meshed two kinds of flanks engagements, i.e. Operating pressure angle α of main active side that presented different operating pressure angle and different transverse contact ratios with the flank profil of non-working side t' gOperating pressure angle α with non-working side side flank profil t' fDifference, α t' g≠ α t' fThe transverse contact ratio ε of main active side α gTransverse contact ratio ε with non-working side α fDifference, ε α g≠ ε α f' 18 °～40 ° of the scopes of Operating pressure angle, the difference of the Operating pressure angle of active side and non-working side is 6 °～15 °, also can break through this scope (referring to Fig. 3, Fig. 4) during special requirement.
The basic parameter of 2. every side flank profil all is not subjected to the restriction of the parameter of traditional design, and special projecting point is: flank profil is long flank profil, addendum coefficient han *Be not equal to 1, usual range is han *＞1.0～1.45.
This asymmetric long flank profil gear promptly can be a spur gear, also can be helical gear; Promptly can be used for the outer gearing transmission, also can be used for interior engagement driving (referring to Fig. 5, Fig. 6).The degree of asymmetry of the selection of main active side flank profil and both sides flank profil depends on actual demand.
Addendum coefficient han *Value also be to depend on actual demand.When being main target, should get low slightly addendum coefficient, big as far as possible active side pressure angle with raising intensity; When being main target with the reduction noise, should get higher addendum coefficient, slightly little active side pressure angle with the stationarity that improves running.Thereby this asymmetric long flank profil gear is guaranteeing that main active side flank profil is surmounting under the situation of the conventional gear limit, have more desirable pressure angle and contact ratio than the wide design of symmetrical full-height tooth, bigger design flexibility has also been taken into account and has been had balanced gear teeth rigidity and good tooth root state.
Particularly, application of the present utility model is mainly following three aspects:
1) in order to improve intensity, when strengthening the Operating pressure angle of active side as far as possible, as active side, the Operating pressure angle maximum might be got more than 40 ° with the large pressure angle side;
2) satisfied when intensity, in order to increase stationarity, to reduce noise, when strengthening the contact ratio of active side as far as possible, can be with little pressure angle side as active side.This is more in the straight-tooth Gear Planet Transmission sees, owing to there is not Face contact ratio, pressure angle by reducing active side and the double action that increases tooth depth increase transverse contact ratio just becomes the effective means that reduces noise.At this moment the Operating pressure angle of active side might be controlled at below 15 °, and the transverse contact ratio of active side might be greater than more than 2 more for a long time for the number of teeth, and the Operating pressure angle that suitably strengthens non-working side mainly is to guarantee resistance to flexure for increasing thickness at root of tooth.
3) common situation is: when improving intensity, also will increase stationarity, reduce noise, in the Operating pressure angle that strengthens active side as far as possible, also take into account the contact ratio that strengthens active side as far as possible.
Confirm feasibility of the present utility model for further theoretically, and be enforcement establish a firm foundation from now on that the claimant extremely is ready to disclose following ins and outs:
1, design method and relevant calculation formula
The utility model adopts the comprehensive Design method of the involute gear of claimant's proposition to carry out asymmetric long tooth Profile Design.
At first, adopt some to carry out designing and calculating with the uncorrelated formula of counterpart rack parameter (being designated hereinafter simply as " Direct Design Method "), so that the design of gear parameter surmounts the restriction of traditional counterpart rack design method (being designated hereinafter simply as " traditional design method ") by what involute engagement basic principle directly derived.
But, because Direct Design Method century-old practice test on the process that is far from aspect the mathematical modeling is so perfect and complete with the traditional design method that development accumulates, still be difficult to have of one's own integral framework, go design gear all having difficulty aspect implementing and applying by Direct Design Method fully.
Therefore, the claimant has proposed the comprehensive Design method of involute gear, it is served as theme with Direct Design Method, be transited into nonstandard cutter processing parameter by conversion, intert all calculating, finally reach the effect of Direct Design Method by traditional design method parameters calculated by the formula that the traditional design method is calculated.Facts have proved that employing should method is simple, calculated data is correct, reliable results, directly perceived.
Relevant its parametric definition schematic representation is seen Fig. 7.Definition of being of no use is cusp and point circle in one of them traditional design: the intersection point that gear teeth normal plane (or end face) is gone up the both sides involute is called cusp, and cusp place circle is called the point circle.
The formula of the traditional design method that the utility model adopts is omitted, the relevant formula of used Direct Design Method (comprising) of listing below and briefly derive from derivation formula, though indivedual formula and traditional formula have repetition, in order to quote the continuity of convenient and logic, also enumerate out in the lump at this.
Following formula is applicable to spur gear and helical gear transverse parameters.In order to simplify and facilitate, used code name is represented with the transverse parameters code name after the helical gear displacement entirely.The used subscript of code name 1, 2Represent little, gearwheel respectively, subscript g, fRepresent active side and non-working side flank profil respectively, subscript ' expression pitch circle running parameter.
(1) Profile angle (pressure angle) calculates
Definition (Fig. 8) by involute can get, (the place circular diameter d of any point Y on the involute Y) Profile angle located can be obtained by formula (1).
α Y＝arccos(d b/d Y) (1)
In the formula: d b-base circle diameter (BCD);
Then the Profile angle (pressure angle) of being had a few on the involute from the cusp to the basic circle can be described with the relation of formula (1):
Cusp (sharp circular diameter d j) Profile angle (wedge angle) located
α j＝arccos(d b/d j) (1a)
d j＝d b/cosα j (1aa)
Top circle (diameter d a) pressure angle
α a＝arccos(d b/d a) (1b)
The pressure angle of standard pitch circle (diameter d)
α t＝arccos(d b/d) (1c)
When helixangle=0, α=α n=α t
When two gear engagement, the working pressure angle (being Operating pressure angle) of pitch circle (diameter d ')
α t’＝arccos(d b/d’) (1d)
cosα t＝(d’/d)cos α t’ (1e)
(2) the external tooth transverse tooth thickness is calculated
By Fig. 9, external tooth is in radius r YThe transverse tooth thickness S at place YWith radius r xThe known transverse tooth thickness S at place xThe pass be:
(S Y+d Y?invα Y)/(S x+d xinvα x)＝d Y/d x
Arbitrfary point Y (diameter d Y) the transverse tooth thickness S that locates YFor:
S Y＝d Y·(S x/d x+invα x-invα Y) (2)
The transverse tooth thickness S at cusp place j=0,
∴S x/d x+invα x-invα j＝0
invα j＝S x/d x+invα x (3)
As known addendum thickness S a, tip diameter d a, tooth top pressure angle α aAsk wedge angle α jThe time
invα j＝S a/d a+invα a (3a)
As known wedge angle α j, tip diameter d a, tooth top pressure angle α aAsk addendum thickness S aThe time
S a＝d a·(invα j-invα a ) (3b)
When known thickness on pitch circle S ', pitch diameter d ', pitch circle meshingangle t' when asking wedge angle
invα j＝S’/d’+inv(α t’) (3c)
As known wedge angle α j, pitch diameter d ', pitch circle meshingangle t' when asking thickness on pitch circle S '
S’＝d’·(invα j-invα t’)
＝(invα j-invα t’)·db/cosα t’?(3d)
(3) the internal tooth transverse tooth thickness is calculated
For internal gear (always as second gear that is meshed, code name subscript 2), the method for available similar external tooth derives the relation of wedge angle and known transverse tooth thickness point X, sees figure 10.
The diameter of intersection point circle (point circle) of going up the both sides involute when internal gear gear teeth normal plane (or end face) is set up with the relation of following formula (4)～formula (4d) during more than or equal to base circle diameter (BCD) (the general work pressure angle all can satisfy greater than 20 ° situation).In order to distinguish, this point circle can be described as little point circle, and diameter is with d Ji2Expression, wedge angle is with α Ji2Expression.
Invα ji2＝invα x2-S x2/d x2 (4)
As known addendum thickness S A2When asking wedge angle etc. parameter
Invα ji2＝invα a2-S a2/d a2 (4a)
When parameters such as known wedge angle are asked addendum thickness S A2The time
S a2＝d a2·(invα a2-inv ji2) 4b)
When parameters such as known thickness on pitch circle S ' are asked wedge angle
Invα ji2＝invα t’-S 2’/d 2’ (4c)
When parameters such as known wedge angle are asked thickness on pitch circle S 2' time
S 2’＝d 2’·(invα t’-invα ji2)
＝(invα t’-invα ji2)·d b2/cosα t’ (4d)
When the Operating pressure angle of internal gear hour (less than 18 ° time might take place), gear teeth normal plane (or end face) is gone up the diameter of the intersection point circle (point circle) of both sides involute can be less than base circle diameter (BCD), and then the relation of formula (4)～formula (4d) is no longer set up.The point circle of the identical external gear of available involute profile this moment is asked the transverse tooth thickness of this internal gear, and sets up the then relation of formula (5)～formula (5d), and the point circle of this moment can be described as big point circle, and diameter is with d Jo2Expression, wedge angle is with α Jo2Expression.
Invα jo2＝invα x2-S x2/d x2+/z 2 (5)
In the formula: z 2The number of teeth for internal gear.
As known addendum thickness S A2When asking wedge angle etc. parameter
Invα jo2＝invα a2-S a2/d a2+π/z 2 (5a)
When parameters such as known wedge angle are asked addendum thickness S A2The time
S a2＝d a2·(invαa 2-invα jo2+π/z 2) (5b)
When parameters such as known thickness on pitch circle S ' are asked wedge angle
Invα jo2＝invα t’-S 2’/d 2’+π/z 2 (5c)
When parameters such as known wedge angle are asked thickness on pitch circle S 2' time
S 2’＝d 2’·(invα t’-invα jo2+π/z 2)
＝(invα t’-invα jo2+π/z 2)·db 2/cos?α t’(5d)
(4) the base circular thickness S of external tooth bCan derive by Fig. 8:
S b＝invα j·d b (6)
(5) a pair of gear does not have the sideshake meshing condition:
p’＝S 1’+S 2’ (7)
In the formula: p '-pitch circle tooth pitch;
p’＝π·d 1’/z 1＝π·d 2’/z 2 (7a)
d 1', d 2'-little, gearwheel pitch diameter
S 1', S 2'-little, gearwheel thickness on pitch circle, the external tooth opinion can be calculated by formula (3d), and the internal tooth opinion can be by formula (4d) and (5d) calculating.
(6) a pair of asymmetric flank profil gear does not have the sideshake meshing condition
To outer gearing
invα t’ g+invα t’ f＝〔invα j1f+invα j1g+u·(invα j2g+invα j2f)-
2·π/z 1〕/(1+u) (8)
Internally engagement
invα t’ g+invα t’ f＝〔u·(invα j2g+invα j2f)-invα j1f-invα j1g+
2·π/z 1〕/(u-1) (8a)
In formula (7), the formula (7a): u-gear ratio, u=z 2/ z 1
(7) root diameter d F1, d F2
To outer gearing:
The root diameter d of small gear F1=2 * (a '-d A2/ 2-C n) (9)
The root diameter d of gearwheel F2=2 * (a '-d A1/ 2-C n) (9a)
Internally engagement:
The root diameter d of small gear F1=2 * (d A2/ 2-a '-C n) (9b)
The root diameter d of gearwheel F2=2 * (d A1/ 2+a '+C n) (9c)
In the formula: C n-bottom clearance;
A '-centre distance.
The root diameter of planet wheel is pressed sun gear and planet wheel engagement calculating in the planetary pinion transmission.
(8) the transverse tooth thickness parameter of asymmetric flank profil gear
The actual addendum thickness S of asymmetric flank profil gear a=(S Ag+ S Af)/2 (10)
The thickness on pitch circle S ' of asymmetric flank profil gear=(S ' g+ S ' f)/2 (11)
The base circular thickness S of asymmetric flank profil gear b=(S Bg+ S Bf)/2 (12)
In the formula, subscript gWith fBe expressed as by the same picket circle, respectively by active side pressure angle and non-working side pressure angle, by the relevant transverse tooth thickness value of symmetrical flank profil calculating.
(9) measurement size of asymmetric flank profil gear
The base tangent length W of asymmetric flank profil gear k=(W Kg+ W Kf)/2 (13)
In the formula, calculate W KgAnd W KfThe time the number of teeth k that strides must be identical.
The length bar span of asymmetric flank profil gear (M value)
M＝(M g+M f)/2 (14)
In the formula, calculate M gAnd M fThe time length bar diameter d p value must be identical.
In the formula, subscript gWith fRepresent the corresponding measurement size numerical value when active side, non-working side calculate by symmetrical flank profil respectively.
2, design procedure
The design procedure that the utility model is big is identical with common epicyclic gearbox.After the basic parameter of each grade is determined, carry out asymmetric long flank profil design of gears respectively to every grade.Distinguish by structure at different levels, mainly contain following two types:
The design of planetary stage gear comprises sun gear-planet wheel outer gearing, the interior engagement of planet wheel-internal gear;
The design of parallel axes level gear is a pair of externally-engaged cylindrical gear pair.
Though the emphasis to design of gears at different levels is different, the unit of engagement and outer gearing two type gear pairs in the gear of whole gear-box always can be divided into.Below, set forth the design procedure of the asymmetric long flank profil gear pair of this two class.
1) known parameters:
A '-centre distance;
z 1, z 2-small gear, the gearwheel number of teeth;
2) tentatively determine active side Operating pressure angle α t' expected value or transverse contact ratio ε αExpected value.
3) calculate or press than the smaller value of pressure angle of expectation and just decide active side pressure angle and non-working side pressure angle α by formula (1e) n, with the selected modulus m of traditional design method n, helix angle, both sides are calculated modification coefficient and relevant gear parameter respectively.
Relatively whether Operating pressure angle or transverse contact ratio reach expected value.Relatively addendum thickness and slip ratio are adjusted pressure angle α n, modification coefficient, addendum.
Addendum thickness Sa=～0.15m by selected large pressure angle side nDetermine tip diameter (when calculated respectively both sides, the tip diameter value should be identical), this step has promptly been determined addendum and addendum coefficient, does not calculate necessity of addendum coefficient during calculating.
4) with conventional method two lateral tooth flanks are calculated relevant gear parameter by symmetrical flank profil respectively by last adjusted value: pressure angle α n, modulus m n, tip diameter d a, root diameter d f(by formula 9～9c), addendum thickness S a, base circle diameter (BCD) d b, basic tooth pitch p b, standard pitch diameter d, pitch diameter d ', modification coefficient x, meshingangle t', transverse contact ratio ε α, slip ratio ζ, the engagement initial circular diameter d E, base tangent length (internally GearFor length bar apart from the M value),.And make of conventional method and to interfere checking computations.
5) two lateral tooth flanks are calculated following gear parameter by symmetrical flank profil respectively: calculate top circle pressure angle α by formula (1b) a, by formula (3a), formula (4a) or (5a) calculate involute function inv (α j), and then obtain wedge angle α j, calculate sharp circular diameter d by formula (1aa) j
6) ask the intersection point of asymmetric flank profil gear both sides flank profil, i.e. the sharp circular diameter d of asymmetric flank profil jAsk method:, relatively save 5 to each gear) corresponding sharp circular diameter d during 2 pressure angles of trying to achieve jSize, press α nSize, at large and small d jBetween given certain diameter d of interpolation JS, obtaining tip diameter respectively is d JSThe time addendum thickness S Ag, S AfAt this moment, the tooth top of large pressure angle is thick to be negative value, the tooth top of little pressure angle is thick be on the occasion of.Adjust diameter d JsSize, the point (this result iterating through about 3 times can obtain) that finds tooth top thick absolute value in both sides to equate is the intersection point of asymmetric flank profil gear both sides flank profil, promptly tries to achieve asymmetric flank profil gear point circular diameter d j
7) by the sharp circular diameter d of asymmetric flank profil gear j, two lateral tooth flanks are pressed symmetrical flank profil respectively: calculate wedge angle α by formula (1a) j, (3b 4b) calculates tip circle transverse tooth thickness S by formula a, by formula 6) calculate the base circular thickness S of external tooth b, calculate parameter such as thickness on pitch circle S ' by formula (3d, 4d or 5d).
8) press the actual addendum thickness S that formula (10)～formula (14) is calculated asymmetric flank profil gear a, thickness on pitch circle S ', base circular thickness S bAnd measurement size W or M value.
9) check meshing condition by formula (7) and formula (8,8a).
3, relevant explanation and discussion:
(1) when the cutter of asymmetric long flank profil or mold design, guarantee that the gear two sides generates the involute length h of flank profil FBe greater than the needed involute length h of engagement E(be that the initial circular diameter of external gear involute is less than the initial circular diameter of engagement, the initial circular diameter of internal gear involute is greater than the initial circular diameter of engagement) so there is not the meshing interference problem, no longer needs to do the meshing interference checking computations during design gear.
(2) according to artificer's experience, addendum thickness S aDesirable: normalizing or modified gear S a＞0.2m n, the desirable 0.15m of special circumstances nCarburizing and quenching gear S a＞0.28m n, the desirable 0.25m of special circumstances nThe design presses the symmetrical flank profil S of large pressure angle aBy～0.15m nAfter choosing tip diameter, the addendum thickness of final asymmetric flank profil all can be greater than the limiting value of above regulation, during design, and can be according to self experience adjustments.
(3) bottom clearance is guaranteeing should to get smaller value as far as possible, to reduce the tooth root flexural stress under tooth top and the teeth groove condition that does not brush up against enough oil storage space mutually in service.The general 0.25m that presses nEnough, during design, can rule of thumb adjust.
(4) the tooth root circular arc at bi-side different pressures angle excessively can excessively realizing by cutter teeth tip circle degree of slipping over and mould tooth root circular arc.Also can pass through analysis means, be designed to other curve, with better reduction tooth root flexural stress.
(5) manufacture method of asymmetric long flank profil gear
For plastic gear, cast gear, powder metallurgical gear and extrusion modling gear, make mfg. moulding die according to the geometrical shape of asymmetric long flank profil gear and get final product.
For the gear of machining, but the gear generating cutting tools of design specialized, as gear hob.Hobboing cutter can design with modulus and the pressure angle that conventional method is pressed on the standard pitch circle, add work gear with the displacement method, also can only do less displacement (claimant discusses the difference of two kinds of profiles of tooth that cutter is processed with publishing an article on relevant periodical) when adding work gear by pitch circle work modulus and working pressure angle design.On gear grinding machine, can realize the roll flute of asymmetric long flank profil gear.
The asymmetric long flank profil gear of processing process in, must pay special attention to the directivity sign of gear, as active side and non-working side are got wrong, will cause whole gear to assemble.
Description of drawings
Below in conjunction with accompanying drawing the utility model is further described.
Fig. 1 is the utility model embodiment's a NGW type single-stage planetary gear reducer drive mechanism sketch.
Among the figure: a-sun gear, c-planet wheel, b-internal gear, x-planet carrier, T a-input torque, T x-output torque.
Fig. 2 is sun gear, planet wheel and the internal gear tooth mesh schematic representation of asymmetric long flank profil Gear Planet Transmission.
Among the figure: z a-sun gear, z c-planet wheel, z b-internal gear.
Fig. 3 is asymmetric external gear flank profil schematic representation.
Fig. 4 is asymmetric internal gear tooth schematic representation.
Among Fig. 3 and Fig. 4: d Bg-working flank base circle diameter (BCD), d Bf-non-working flank base circle diameter (BCD), d a-tip diameter, d-standard pitch diameter, d j-sharp circular diameter, α Jg-working flank wedge angle, α Jf-non-working flank wedge angle, S-graduated arc thickness.
Fig. 5 is asymmetric flank profil outer gearing transmission schematic representation.
Fig. 6 is an engagement driving schematic representation in the asymmetric flank profil.
Among Fig. 5 and Fig. 6: z 1, z 2-little, gearwheel, d B1g, d B2g-little, gearwheel working flank base circle diameter (BCD), d B1f, d B2f-little, gearwheel non-working flank base circle diameter (BCD), α t' g-working flank working pressure angle, α t' f-non-working flank working pressure angle.
Fig. 7 is an involute profile parameter-definition schematic representation.
Among the figure: d b-base circle diameter (BCD), d a-tip diameter, d j-sharp circular diameter, α a-top circle pressure angle, α j-wedge angle, S a-addendum thickness, S b-base circular thickness.
Fig. 8 is an involute basic geometric relationship schematic representation.
Among the figure: r b-Base radius, r YY point place circle radius on the-involute, α YY point pressure angle on the-involute, ζ Y-U and T YBetween roll angle, ζ Y=tan α Y
Fig. 9 is the transverse tooth thickness calculating chart of any radius on the external gear involute profile.
Among the figure: r b-Base radius, r x-known transverse tooth thickness circle radius, r Y-any circle radius, r j-sharp circle radius, S x-radius r xKnuckle-tooth is thick, S Y-radius r YKnuckle-tooth is thick, α j-wedge angle, α x-radius r xThe pressure angle at place, α Y-radius r YThe pressure angle at place.
Figure 10 is the transverse tooth thickness graph of a relation of internal gear involute profile.
Among the figure: r B2-Base radius, r A2-Outside radius, r X2-known transverse tooth thickness circle radius, r Ji2-little sharp circle radius, r Jo2-big sharp circle radius, S A2-top circle transverse tooth thickness, S X2-radius r xKnuckle-tooth is thick, α Ji2-little point circle wedge angle, α Jo2-big point circle wedge angle, α X2-radius r X2The pressure angle at place, α A2-top circle pressure angle.
Embodiment
Describe above design method in detail below by specific embodiment.
Embodiment one
Present embodiment is a NGW type single-stage planetary gear reducer as shown in Figure 1.Retarder input speed 1500r/min, output speed 202r/min, reduction speed ratio 7.41: 1, rated power 200kW.Wherein, planet wheel is fixed, and torque is imported by sun gear, drives the output shaft output that planet carrier connects through planet wheel.This device is mainly one-way only operation, and main sense of rotation is clear and definite, the time of reverse operation seldom and the load very low.Because size restrictions wishes to have improved as far as possible bearing capacity, and reduce the noise and the vibration of gear-box.
According to desired speed ratio, this retarder can only adopt the structure of 3 planet wheels.
Consider certain batch, in order to satisfy above user demand, present embodiment is when adopting carburizing and quenching gear, further adopted asymmetric spool gear flank profil, by suitable weakening non-working side and increase addendum, strengthen the bearing capacity of active side, make the bearing capacity of this gear-box exceed the limit of conventional design, and reach the noise of reduction gear-box and the effect of vibration.The design and calculation method of asymmetric long flank profil gear of outer gearing and the asymmetric long flank profil gear of interior engagement can be introduced simultaneously by example of present embodiment, all gear pairs of various gear-boxes of the present utility model can be contained as infrastructure elements.
Designed gear-box basic parameter sees Table 1, and the sun gear of Gear Planet Transmission, planet wheel and internal gear tooth mesh schematic representation are seen Fig. 2.
The basic parameter of table 1 gear-box
Figure BSA00000340592400161
Design can be according to the following steps:
1) determines several basic parameters: centre distance a '=97.5mm with planetary traditional design method; Sun gear, planet wheel, internal gear number of teeth z a=17, z c=46, z b=109; The actual transmission of retarder compares i=1+z b/ z a=1+109/17=7.412; Modulus m n=3mm; Facewidth b=48mm.Above parameter is promptly as the design's known parameters.
2) set expected value
Because planet wheel z c-internal gear z bInterior engagement be male and female face engagement, its contact stress is less than sun gear z a-planet wheel z cContact stress during outer gearing.The active side of sun gear-planet wheel outer gearing should be selected higher Operating pressure angle, sets its α t' expected value be～32 °, transverse contact ratio ε αExpected value 〉=1.2.The active side Operating pressure angle α of engagement in planet wheel-internal gear t' expected value be～25 °, transverse contact ratio ε αExpected value 〉=1.2.
Because planet wheel is a two-way working, its z a-z cThe non-working surface of engagement is exactly z c-z bThe working surface of engagement.In order to take into account z c-z bThe intensity of engagement, its z a-z cThe non-working surface of engagement also will be got enough big working pressure angle.
For the design of parallel axes level gear, its program and method and sun gear z a-planet wheel z cThe externally-engaged cylindrical gear pair is roughly the same.Because do not need to take into account interior mesh parameters as planet wheel, the degrees of freedom of choosing of working surface working pressure angle can be bigger.When being major heading with raising intensity, as long as the life-span of bearing is enough, the working pressure angle of non-working surface can obtain littler (as below 18 °), and the working pressure angle of working surface can obtain bigger (as more than 40 °).When increasing contact ratio and be main design object, the working pressure angle of two faces can be less than 20 °, and variant, a side perhaps arranged greater than 20 °.
3) just decide pressure angle
By formula (1e) calculating, during the Operating pressure angle of the value of meeting the expectation, large pressure angle side α n=28.96 °, little pressure angle side α n=20.76 °.Just decide z a-z cOuter gearing active side pressure angle α n=30 °, non-working side pressure angle α n=22.5 °, z then c-z bInterior joggleword side pressure angle α n=22.5 °, non-working side pressure angle α n=30 °.
4) sun gear z a-planet wheel z cThe designing and calculating of external gear pump pair
(1) equals 1 by addendum coefficient earlier, both sides are calculated modification coefficient and relevant gear parameter respectively with traditional design method.Result of calculation is: active side Operating pressure angle α t'=32.9254 ° meet the demands; Transverse contact ratio ε α=1.228, though meet the requirements, but still feel on the low side.The both sides slip ratio is all lower.The addendum thickness Sa of non-working side is thicker.Press the active side addendum thickness Sa=～0.15m of large pressure angle nControl increases addendum, and adjusting tip diameter (the both sides value is identical) at last is d A1=59.8mm, d A2=147.8mm.
(2) with conventional method two lateral tooth flanks are calculated relevant gear parameter (root diameter d wherein by symmetrical flank profil respectively by adjusted value fBy formula 9～formula 9c), see Table 2.Simultaneously, carry out the correlation interference checking computations.
Table 2z a-z cExternal gear pump second parameter 1
The data of numerical value in the table 2 except that the thick and base tangent length of tooth top all can be used as the final data of unsymmetrical profile contour gear.
(3) two lateral tooth flanks are calculated following gear parameter by symmetrical flank profil respectively, see Table 3:
Table 3z a-z cExternal gear pump second parameter 2
(4) ask the intersection point of asymmetric flank profil gear both sides flank profil, i.e. the sharp circular diameter d of asymmetric flank profil j
According to the calculated value of table 3, to the sharp circular diameter d of sun gear by 30 ° of pressure angles calculating of symmetrical flank profil j=60.2673mm, 22.5 ° of sharp circular diameter d that pressure angle calculates j=61.3105mm, the sharp circular diameter during unsymmetrical profile contour should be between this two value.Press α nSize, at large and small d jBetween given certain d of interpolation JS, obtaining top circle respectively is d JSThe time addendum thickness S Ag, S Af, at this moment, the transverse tooth thickness of large pressure angle is a negative value, the transverse tooth thickness of little pressure angle be on the occasion of.Adjust diameter d JsSize, the point that finds both sides transverse tooth thickness absolute value to equate is the intersection point of asymmetric flank profil gear both sides flank profil.This example is worked as d JSDuring=60.753mm, S Ag=-0.4567mm, S Af=0.4569mm, the only poor 0.0002mm of two values; Same quadrat method to planet wheel, is worked as d JSDuring=149.261mm, S Ag=-0.6387mm, S Af=0.6381mm, the only poor 0.0006mm of two values has very high precision.The sharp circular diameter of promptly trying to achieve asymmetric flank profil sun gear and planet wheel is respectively 60.753mm and 149.261mm.
(5) by the top sharp circular diameter d that asks asymmetric flank profil gear j, two lateral tooth flanks are calculated wedge angle α by symmetrical flank profil respectively jEtc. parameter, see Table 4.
Table 4z a-z cExternal gear pump second parameter 3
Figure BSA00000340592400191
(6) relevant parameter of the asymmetric flank profil gear of calculating:
Sun gear:
Try to achieve addendum thickness S by formula (10) A1=(0.878+0.745)/2=0.816mm
Try to achieve thickness on pitch circle S by formula (11) 1'=(6.0369+4.9977)/2=5.517mm
Try to achieve base circular thickness S by formula (12) B1=(8.287+6.161)/2=7.224mm
Try to achieve base tangent length W=(32.4414+32.6375)/2=32.539mm by formula (13)
Stride number of teeth k=4.
Planet wheel: can try to achieve equally
Addendum thickness S A2=(1.073+0.869)/2=0.971mm
Thickness on pitch circle S 2'=(4.6919+3.7219)/2=4.2069mm
Base circular thickness S B2=(12.651+7.895)/2=10.273mm
Base tangent length W=(77.4362+78.0987)/2=77.767mm
Stride number of teeth k=9.
(7) check meshing condition
Two-wheeled thickness on pitch circle sum S 1'+S 2'=5.517+4.2069=9.7239mm
By formula (7a) pitch circle tooth pitch p '=π d 1'/z 1=9.724mm
Formula (7) p '=S 1'+S 2' set up, meet no sideshake meshing condition.
Check with formula (8), the substitution respective value is calculated, formula (8) left end=0.10868; Formula (8) right-hand member=0.10868; The left and right terminal number value of formula (8) equates that no sideshake meshing condition is correct.
5) planet wheel z c-internal gear z bThe designing and calculating of internal gear pair
Process and joint 4) middle sun gear z a-planet wheel z cThe designing and calculating of external gear pump pair is similar, repeats no more, the relevant table 5～table 7 that the results are shown in.Only particular point is described as follows:
(1) calculate in during engagement the parameter and the outer gearing of planet wheel identical, just changed the direction of active side.
(2) the little sharp circular diameter of the internal gear of present embodiment is greater than base circle diameter (BCD), and the formula calculating relevant with little point circle has related parameter.
At first, with conventional method two lateral tooth flanks are calculated relevant gear parameter by symmetrical flank profil respectively, see Table 5 by adjusted value through tentative calculation.Simultaneously, carry out the correlation interference checking computations.
Table 5z c-z bInside engaged gear second parameter 1
Figure BSA00000340592400211
The final data that numerical value in the table 5 is thick except that tooth top, the data W and the M value all can be used as the unsymmetrical profile contour gear.
The top circle pressure angle α that two lateral tooth flanks are calculated by symmetrical flank profil respectively aEtc. parameter, see Table 6.
Table 6z c-z bInside engaged gear second parameter 2
Figure BSA00000340592400221
Obtain the intersection point of asymmetric flank profil gear both sides flank profil, the sharp circular diameter dj of asymmetric flank profil planet wheel and internal gear is respectively 149.261mmmm and 327.234mm.
Sharp circular diameter d by the asymmetric flank profil gear of ask j, two lateral tooth flanks are calculated wedge angle α by symmetrical flank profil respectively jEtc. parameter, see Table 7.
Table 7z c-z bInside engaged gear second parameter 3
Figure BSA00000340592400222
Calculate the relevant parameter of asymmetric flank profil gear at last:
Planet wheel: outer gearing is tried to achieve.
Internal gear:
Addendum thickness S A2=(1.189+1.635)/2=1.412mm
Thickness on pitch circle S 2'=(4.7131+6.3214)/2=5.517mm
Stride rod apart from (dp=5.1mm), M=(329.453+329.133)/2=329.293mm.
And check meshing condition:
S 1’+S 2’＝4.2069+5.517＝9.7239mm
By formula (7a) p '=π d 1'/z 1=9.724mm
Formula (7) p '=S 1'+S 2' set up, meet no sideshake meshing condition.
Check with formula (8a), the substitution respective value is calculated; Formula (8a) left end=0.10868; Formula (8a) right-hand member=0.10868; The left and right terminal number value of formula (8a) equates that no sideshake meshing condition is correct.
Intensity had a more substantial increase after this embodiment adopted asymmetric long flank profil design of gears, and contact ratio and overlap ratio has obvious increasing, and meshing quality improves, and noise reduces.
In a word, the utility model is studied by long-term practice, according to rigorous theory analysis, a kind of involute planet gear case of asymmetric long flank profil gear structure of the standard that breaks traditions has been proposed, the asymmetric long flank profil gear that it adopts, broken through the restriction of the standardization Basic rack parameter of traditional design, improve gear capacity or weight reduction, increasing contact ratio to strengthen main stand under load side flank profil and to increase the double action of addendum, to reach, improve transmission performance, reduce the effect of running noise and vibration by the flank profil that weakens non-stand under load or be subjected to the underloading side.
The asymmetric long flank profil gear of this involute planet gear case promptly can be a spur gear, also can be helical gear; Promptly can be the single-stage planetary transmission, also can be the multistage planet transmission, also can be the multistage planet transmission that one-level or two-stage cylindrical gears and one or more levels planet are formed.The selection of main stand under load side flank profils at different levels and the degree of asymmetry of both sides flank profil and the value of addendum depend on actual demand.

Claims (6)

1. asymmetric long flank profil involute planet gear case, have the input shaft and the output shaft that connect by the gear transmission that is meshing with each other, the gear of described gear-box has the gear teeth that are uniformly distributed along the circumference, described gear teeth both sides are involute profile, it is characterized in that: the involute profile of described gear teeth both sides is generated by the different basic circle of diameter, and the difference of the Operating pressure angle at described gear teeth active side and non-working side pitch circle place is 6 °～15 °.
2. asymmetric long flank profil involute planet gear case according to claim 1 is characterized in that: the addendum coefficient of the described gear teeth is greater than 1.0, smaller or equal to 1.45.
3. asymmetric long flank profil involute planet gear case according to claim 1 and 2 is characterized in that: during the Operating pressure angle of described gear teeth active side 〉=30 °, the transverse contact ratio of active side is 1.2～1.5.
4. asymmetric long flank profil involute planet gear case according to claim 1 and 2 is characterized in that: during the Operating pressure angle of described gear teeth active side＜18 °, the transverse contact ratio of active side is 1.8～2.5.
5. asymmetric long flank profil involute planet gear case according to claim 1 and 2 is characterized in that: the mutual outer gearing of described gear, the root diameter d of its gear teeth F1,2Pressing following formula determines:
d f1、2＝2×(a’-d a2、1/2-C n)
In the formula
d F1,2---the root diameter of small gear, gearwheel
A '---centre distance
d A2,1---the tip diameter of gearwheel, small gear
Cn---bottom clearance is determined by 0.25 modulus (mn).
6. asymmetric long flank profil involute planet gear case according to claim 1 and 2 is characterized in that: the interior mutually engagement of described gear, the root diameter d of its gear teeth F1,2Pressing following formula determines:
d f1＝2×(d a2/2-a’-Cn)
d f2＝2×(d a1/2+a’+Cn)
In the formula
d F1, df2---the root diameter of external gear, internal gear
A '---centre distance
d A1, da2---the tip diameter of external gear, internal gear
Cn---bottom clearance is determined by 0.25 modulus (mn).
CN2010205998276U 2010-10-31 2010-10-31 Asymmetric long-tooth profile evolvent planetary gear box Expired - Fee Related CN201851630U (en)

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